In the field of measurement, it is useful to characterize devices. In this context, a device is defined as a network containing ports. The behavior of the device can be described as the relationship between signals on ports and how these signals are affected as they pass through the various ports of the device. The device that is being characterized is termed the device under test or DUT.
As is known to those of ordinary skill in the art of high-speed electronics, a useful method of describing a system is through the provision of scattering parameters (S-parameters). As is known to those skilled in the art of microwave measurements, S-parameters define the port-to-port relationship of a network in the relationship Sa=b where S is a complex matrix that is provided for a variety of frequencies, a is a vector of incident waves on the device ports and b is a vector of reflected waves. There are many different types of network parameters such as Y, ABCD, Z, etc. Mostly, these types of network parameters are interchangeable and are simply different ways of describing similar behavior.
The characterization of devices is preferably performed using network analyzers, although other methods of characterization may be appropriate. Network analyzers launch waves into a device and measure the reflected waves. This is accomplished either by generating and measuring sinusoids at a given frequency, as in the vector network analyzer (VNA) or by launching and measuring reflected fast rise-time pulses, steps, or impulses as in time-domain reflectometry (TDR). Either way, the same information is obtained.
One particular difficulty that arises is that both the system and the testing device are actual, physical systems. In any such system often the connections that are made to the VNA or TDR are restricted because these systems must be built for general purpose use, and are designed in advance of any particular measurement desired by a particular user at a particular time. Often, connection methods are restricted to coaxial connections or the sex of the connection is restricted to either male or female. Therefore, if the device being characterized does not employ the required connectors, then an adapter or fixture must be created to connect the device to the measurement instrument. This fixture must either be of such high quality that it can be neglected, or it must be de-embedded from the measurement, thus allowing the user to characterize the system as if the fixture and measurement devices did not exist. De-embedding, in this context, is therefore the act of undoing or removing the effects of known fixturing or other elements to extract only the measurement of interest, and to insure that this measurement is free of any influence imposed by the measurement system or technique employed.
Even if the measurement instrument connections can be adapted to the DUT, usually these instruments are calibrated prior to use using a variety of methods, most involving the use of known standards or known relationships in standards. Standards usually come in specific forms, the most generally used being coaxial calibration standard kits or electronic calibration modules that are also coaxial in connection method. Therefore, regardless of connection capability to a DUT, often the calibration reference plane is limited to where suitable connection of standards can be made.
Many modern measurement instruments provide methods to gate the measurement. Gating is usually performed as time gating. Time gating is the method whereby the time through various fixtures and connections is known or can be inferred by observation. Gating theoretically moves the reference plane from the calibration and connection point past the fixturing to the boundaries of the DUT. This method does not perform a complete de-embedding in the sense that the entire behavioral model of the DUT cannot be extracted. In other words, gating is used to move the reference plane for some S-parameter measurements but does not move it for all measurements, and therefore does not obtain a complete de-embedded model of the DUT.
The reason that the complete de-embedded model is useful is because, when characterizing devices, one is usually trying to take a measurement that will determine the performance of the device when later used in a different environment. Usually this final performance will be that of the DUT in another system, and therefore it would be beneficial to know how the device will affect the overall performance of that other system. Test and measurement engineers take and analyze measurements that somehow correlate with final performance. Sometimes the measurement is simply a pass-fail test. In these cases, gated measurements are usually good enough. That being said, there are many examples of measurements that are too complex to be handled through this relatively simple method. More importantly, often the aim in the device characterization is to obtain a behavioral model of the device. As stated previously, the network parameters of a device can be thought of as completely defining how the device will perform. Systems are so complex nowadays that often, the way of measuring how a device will perform is to generate a model of the device and use it in a simulation. A simple example of this is in the design of high-speed communication channels. In this case, the S-parameter measurements provide indications of how the channel will perform, but a preferred way is to use a model of the channel in a simulation (along with models of the other components) and actually see how the channel behaves in the simulation, measuring directly the primary criteria like bit error rate, for example. In cases like this, the measurement instrument is required to provide not just a chart or graph, but a usable model. In this case, a gated measurement is not adequate, and to get a truly accurate model, the behavioral model of the DUT needs to be de-embedded from fixturing.
There are many known methods of de-embedding. It is a mathematical exercise. The methods involve first measuring a system from its periphery. In other words, a system is measured containing (known) fixtures and the (unknown) DUT. Then, attempts are made to mathematically remove known elements portion by portion. Prior approaches of de-embedding can be broadly divided into two categories. In one approach, de-embedding proceeds by converting S-parameters of the system and known elements to some form of cascadable parameters e.g. T-parameters, ABCD parameters etc., inverting these parameter matrices and multiplying them by the measured parameters of the system. Despite the fact that many methods exist for doing this, it is a problematic exercise. Sometimes, the nature of the system makes this process difficult, such as when systems of even or odd numbers of ports are involved. The application of cascadable parameter techniques to de-embedding is situational. In other words, each de-embedding problem is a new problem to be solved and requires a special strategy that depends on each new topology encountered.
In U.S. Pat. No. 6,744,262, article Application Note Embedding/De-embedding—Simulated removal and insertion of fixtures, matching and other networks, November 2001, and U.S. Pat. No. 6,665,628, the measured S-parameters of the system are converted into T-parameters. The system T-parameters are then written as a cascade of known fixture T-parameters and unknown DUT T-parameters. The DUT is then de-embedded by inverting the T-parameters of the fixtures. Such a method has several drawbacks. The conversion to T-parameters requires a careful examination of the circuit configuration and identification of “input” and “output” ports, along with a careful numbering of ports for each different circuit configuration. This makes the algorithm difficult to automate for any given circuit. The conversion also puts a restriction on the number of ports of a DUT e.g it has to be even or divisible by 4 etc.; or a restriction on the nature of fixtures e.g. fixtures are required to have even number of ports. In U.S. Pat. No. 6,961,669, the measured S-parameters are converted into ABCD-parameters. These parameters are carefully partitioned and then arranged in cascade equation to de-embed the unknown DUT. This approach suffers from the same drawbacks as the conversion to T-parameters approach. In general, T-parameter approaches have problems with the numbers of ports and are difficult to automate.
Another category of solutions to this problem involves careful manipulation of the circuit parameters to de-embed the DUT. Such an approach is generally restrictive to certain types of fixtures or for DUTs with fewer ports. Each different circuit model or fixture requires a new set of rules to de-embed the DUT. In the tool RF toolbox, The MathWorks, Natick Mass. only two port DUTs with a certain kind of fixture is considered. U.S. Pat. No. 6,211,541 considers a problem pertaining to integrated circuits (ICs) with specific type of “fixtures”—that arising from the leads of the IC. In article 3.3.4.3 De-embedding techniques with Y, Z, S, A matrices, the explanation is limited to two port networks as the DUT. The “fixtures” considered, are circuits made up of some combination of inductors and capacitors. And de-embedding is performed through clever circuit manipulation. Such a method is difficult to automate, and one needs to look at different fixtures and DUT combinations as new problems to be solved.
In De-embedding techniques in signal integrity: A comparison study, 2005 conference on Information Sciences and System, The Johns Hopkins University, Mar. 16-18, 2005, the authors compare four different techniques of de-embedding. The four techniques are listed here for completeness. G. Antonini, A. Ciccomancini Scogna and A. Orlandi, “S-Parameter Characterization of Through, Blind, and Burned Via Holes,” IEEE Trans. on Mobile Computing, vol. 2, no. 2, April-June 2003 uses the conversion to T-parameters approach described above. J. Song, F. Ling, G. Flynn, W. Blood and E. Demircan, “A De-embedding Technique for Interconnects,” Proceedings of the Electrical Performance of Electronic Packaging, 2001 uses careful manipulation of circuit admittances and impedances. Such methods as pointed out earlier are specific to certain problems and cannot be considered as general solutions. L. V. Hauwermetren, M. Botte and D. De Zutter, “A New De-embedding technique for On-Board Structure Applied to Bandwidth Measurement of Package,” IEEE Trans. On Components, Hybrids and Manufac. Tech., vol. 16, no. 3, May 1993. uses S21 parameter of the system and the fixture to recover the S21 parameter of the DUT. The authors use the Fourier transform property of multiplication in frequency domain instead of convolution in time domain. The obvious drawback is that the other S-parameters of the DUT cannot be recovered using this approach. H. Chang, C. Kuo and T. Wu, “A Time-Domain Approach to Extract SPICE-compatible Equivalent Circuit Models for embedded interconnects”, 2002 IEEE International Symposium on Electromagnetic Compatibility, and C. Schuster and W. Fichner, “Signal Integrity Analysis using the Finite Difference Time Domain (FDTD) method and layer peeling techniques”, IEEE Transactions on Electromagnetic Compatibility, Vol. 42, No. 2, May 2000. use the time gating technique to make measurements in the time-domain.
Another technique is tuning. One can view the problem as one of simulating the S-parameters of the total system in a certain topology and comparing the simulated S-parameters to the known measured S-parameters on the periphery. In this manner, the S-parameters of the unknown DUT can be varied until the simulated S-parameters of the system match. This method is usable and generates the desired results, but it is an iterative process. Iterative processes like this are not guaranteed to converge to an answer. In many cases, the solution is a gradient walk or Newton's method. There is no way to prove that answers obtained in this manner are in fact the best answer possible.
None of the current approaches can handle more than one unknown DUT.
Therefore, the inventors of the present invention have determined that what is needed is a method of measuring a system at its boundaries and solving directly for the network parameters of a single device or multiple unknown devices in a network.
The inventors of the present invention have determined that what is further needed is a method of performing this calculation whereby the user provides only the known measurements of the overall system, a description of the network topology containing the known and unknown elements, and the characteristics of the known devices.
The inventors of the present invention have determined that what is additionally needed is a tool that performs this calculation without reexamination of the topology on each application.
The inventors of the present invention have determined that what is further additionally needed is a method that contains any feasible number of ports.
The inventors of the present invention have determined that none of the calculation methods noted above meet these needs, or other needs of the industry in this area.